Stability of Blaschke's characterization of ellipsoids and Radon norms
type: Item
instance of: scholarly article
title: Stability of Blaschke's characterization of ellipsoids and Radon norms
zbMATH Open document ID: 0887.52002
DOI: 10.1007/PL00009301
published in: Discrete \& Computational Geometry
publication date: 1997-06-04T00:00:00Z
review text: The author presents stability versions of classical characterization results in convex geometry. The first result extends a theorem of Blaschke, it shows that a convex body in \(\mathbb{R}^d\), \(d\geq 3\), which has almost planar shadow boundaries is almost an ellipsoid. The second result proves that a planar convex body which has almost conjugate diameters is close (in the Banach-Mazur distance) to a Radon disk. Some consequences are also given.
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 46C15
zbMATH DE Number: 1016878
zbMATH Keywords: stability results
zbMATH Keywords: shadow boundary
zbMATH Keywords: ellipsoid
zbMATH Keywords: Radon disk
zbMATH Keywords: conjugate diameter
author: Peter M. Gruber
reviewed by: Wolfgang Weil
MaRDI profile type: Publication
full work available at URL: pl00009301
OpenAlex ID: W2009597305
Recommended article: The stability of certain Riemann ellipsoids
Recommended article: Stability properties of the Riemann ellipsoids
Recommended article: Stability of the Blaschke-Santaló inequality in the plane
Recommended article: Stability of the Blaschke-Santaló and the affine isoperimetric inequality
Recommended article: Stability of the reverse Blaschke-Santaló inequality for unconditional convex bodies
Recommended article: Inequalities for radial Blaschke–Minkowski homomorphisms
Recommended article: The Radial Behavior of Blaschke Products
Recommended article: Q4315485
Recommended article: On a Stability Property of the Generalized Spherical Radon Transform
Recommended article: Stability of Radon-Nikodym theorem and its applications
description: scientific article; zbMATH DE number 1016878